Year: 2016
Author: Jerry L. Bona, Min Chen
Journal of Mathematical Study, Vol. 49 (2016), Iss. 3 : pp. 205–220
Abstract
Studied here is the Boussinesq system $$η_t+u_x+(ηu)_x+au_{xxx}-bη_{xxt}=0,$$ $$u_t+η_x+\frac{1}{2}(u²)_x+cη_{xxx}-du_{xxt}=0,$$of partial differential equations. This system has been used in theory and practice as a
model for small-amplitude, long-crested water waves. The issue addressed is whether
or not the initial-value problem for this system of equations is globally well posed.
The investigation proceeds by way of numerical simulations using a computer code
based on a a semi-implicit, pseudo-spectral code. It turns out that larger amplitudes
or velocities do seem to lead to singularity formation in finite time, indicating that the
problem is not globally well posed.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jms.v49n3.16.01
Journal of Mathematical Study, Vol. 49 (2016), Iss. 3 : pp. 205–220
Published online: 2016-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 16
Keywords: Boussinesq systems global well-posedness singular solutions Fourier spectral method nonlinear water wave.
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